In the last years, a very interesting topic has arisen and became the research focus not only for many
mathematicians and statisticians, as well as for all those interested in modeling issues: The Skew normal
distributions’ family that represents a generalization of normal distribution. The first generalization was
developed by Azzalini in 1985, which produces the skew-normal distribution, and introduces the
existence of skewness into the normal distribution. Later on, the extended skew-normal distribution is
defined as a generalization of skew-normal distribution. These distributions are potentially useful for
the data that presenting high values of skewness and kurtosis. Applications of this type of distributions
are very common in model of economic data, especially when asymmetric models are underlying the
data. Definition of this type of distribution is based in four parameters: location, scale, shape and
truncation. In this paper, we analyze the evolution of skewness and kurtosis of extended skew-normal
distribution as a function of two parameters (shape and truncation). We focus in the value of kurtosis
and skewness and the existence of arange of values where tiny modification of the parameters produces
large oscillations in the values. The analysis shows that skewness and kurtosis present an instability
development for greater values of truncation. Moreover, some values of kurtosis could be erroneous.
Packages implemented in software R confirm the existence of a range where value of kurtosis presents
a random evolution.